Projective and generating modules over the ring of pseudorational numbers

The projective, flat, and generating modules over the ring of pseudorational numbers are described. For the projective modules, a complete independent system of invariants is constructed.     

Tri-Hamiltonian Structures of Egorov Systems of Hydrodynamic Type

We prove a simple condition under which the metric corresponding to a diagonalizable semi-Hamiltonian hydrodynamic type system belongs to the class of Egorov (potential) metrics. For Egorov diagonal hydrodynamic type systems satisfying natural semisimplicity and homogeneity conditions, we prove necessary and sufficient conditions under which the third structure is local or corresponds to a metric of constant curvature. The results are illustrated by some well-known physical examples of such systems.     

Phased Antenna Arrays Based on Vircators: Numerical Experiments

We present the results of numerical simulation of two different design schemes for phased antenna arrays (PAAs) based on vircators, i.e., microwave oscillators with virtual cathodes. The active and passive schemes of PAA design are analyzed separately. It is shown that in the case of an active PAA scheme, the degree of tuning the vircator to the master oscillator increases with increasing power of the latter, while in the case of a passive PAA scheme, the coherence degree of two vircators due to waveguide coupling increases with increase in the coupling coefficient.     

Compact acousto-optic filter with beam expanders constituted by photonic crystal rows of airholes

A compact acousto-optic (AO) filter with multireflector (MR) beam expanders constituted by 32 photonic crystal rows of airholes in LiNbO(3) waveguide has been proposed and numerically studied by the two-dimensional finite-difference-time-domain method. The diameter and position of every row of holes are gradually varied along MR beam expanders in order to provide high efficiency and good sidelobe suppression. Device sizes are 70 μm × 150 μm, with an FWHM bandwidth of 4.4 nm, a tuning range of 110 nm, internal loss of -3 dB, and sidelobes of -20 dB, thus providing a unique value of 0.6 μm(2) for the product FWHM bandwidth by an AO length. It is intended for use in fiber optics telecommunications and sensing.     

Mechanisms of broadening of emission lines of a laser-induced plasma generated on the surface of rigid targets

This article reports the results of an experimental investigation of the basic mechanisms that cause the broadening of emission lines of a laser-induced plasma generated on the surface of rigid targets in a gaseous atmosphere. The contribution of Stark and resonance mechanisms of emission-line broadening for the resonance doublet Al I 3s²3p²P_3/2,1/2-3s²4s²S_1/2 and triplet Mg I 3s3p³P _0,1,2 ⁰ -3s4s³S₁ is discussed. The concentrations of neutral Al atoms in the laser-induced plasma are evaluated by the magnitude of resonance line broadening. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 67, No. 2, pp. 234–237, March–April, 2000.     

Sequences of Endomorphism Groups of Abelian Groups

In the paper, Problem 18.3 of the book “Abelian groups” (2015) by L. Fuchs is solved in the case of Abelian groups with finite p-ranks. For an Abelian group A, a sequence of groups (A_n) is considered, where A₀ = A and A_n+1 = End A_n. It is shown that, if all p-ranks of the group A are finite, then this sequence can stabilize either after A₀ or after A₁.

     

Global comparison of finite-dimensional reduction schemes in smooth variational problems

A new criterion for global smooth equivalence of a pair of key functions corresponding to a smooth functional in the calculus of variations for a given pair of finite-dimensional reduction schemes is established. The statement is presented in abstract form (we consider a functional on a Banach space with a Fredholm gradient). The main condition is the possibility to deform the reduction schemes into each other preserving the coercivity of the key functions. As a corollary, we obtain the theorem concerning global smooth equivalence of the key functions calculated by the Lyapunov-Schmidt and Morse-Bott reduction schemes in the two-point boundary value problem for a natural mechanical system of sufficiently general form. Translated fromMatematicheskie Zametki, Vol. 67, No. 5, pp. 745–754, May, 2000.     

Investigation of the mechanical properties of polymer surface layers using surface waves

It is possible to excite ultrasonic surface waves at the surface of polymer materials and to determine the dependence of the wave parameters on the mechanical properties of the surface. The nature of the variation of the surface wave characteristics with material, temperature, and the frequency of the exciting vibrations has been established.Mekhanika Polimerov, Vol. 3, No. 5, pp. 933–939, 1967